Vice President Joe Biden was meeting late Monday with Senate Democrats to brief them on a proposed deal to stop sharp tax increases and spending cuts. A source told NPR the deal with congressional Democratic and Republican leaders includes a mix of both.

Senate Majority leader Harry Reid and House Minority Leader Nancy Pelosi have signed off on the agreement, which calls for a two-month deferral of the automatic spending cuts known as the sequester. The source says the cuts will be paid for half with revenue and half with more targeted spending cuts.

The Senate may vote on the deal Monday night, but there will be no vote in the House until Tuesday at the earliest.

Our original post:

Congress will not succeed in avoiding the "fiscal cliff" before New Year's Day, as the Senate isn't likely to vote on a potential deal until after midnight, and the House of Representatives has adjourned until Tuesday.

The failure comes after lawmakers and the White House spent weeks and months trying to work out a budget deal to avert tax hikes and budget cuts that will kick in automatically in 2013.

The House adjourned just before 6:30 p.m. ET; the chamber's next session will begin Tuesday at noon. A Senate vote on a deal could still come Monday night or early Tuesday. After meeting with other Republicans, Sen. Bob Corker (R-Tenn.) said he thinks "it's highly likely that some time this evening there'll be a vote on the Senate side," writes Ed O'Keefe of The Washington Post.

Corker said he and his fellow senators may vote on a deal after midnight.

"I think they're attempting to get the legislative language in order and vote on it tonight," he said, "you know, 1, 2, 3, 4 in the morning, whatever."

Any deal that is worked out would likely include terms that make it apply retroactively to the time between midnight tonight and the bill's enactment, NPR's Washington Editor Ron Elving tells us.

There are multiple news reports that the key provisions in the emerging deal include increases in income tax rates for families earning more than $450,000 a year and individuals who make more than $400,000. Other Americans' income tax rates would remain unchanged.

House members would want time to read any bill the Senate might offer, reports Reuters, citing "a Republican leadership aide." The aide also says a delay would have only a limited effect on the U.S. economy, as financial markets are closed Tuesday for the New Year's Day holiday.

As NPR's Washington Desk reminds us, legislators on Capitol Hill are also facing another deadline, and this one is beyond their control: At 11:59 p.m. ET Thursday, the 112th Congress will begin its final minute. Any budget crisis that lingers after midnight and into Friday would be the problem of the next Congress.

News that the New Year's Eve deadline might pass without Congress approving a deal follows comments by Senate Minority Leader Mitch McConnell earlier Monday that "we are very, very close" to reaching a deal.

President Obama said this afternoon that an agreement to prevent most Americans' taxes from rising at midnight is "within sight," but not yet done. An hour or so later, McConnell — the key Republican in talks about the so-called fiscal cliff — agreed.

As we've been reporting, there have been signs today of progress in the talks — which are now being led by Vice President Biden and McConnell. The so-called fiscal cliff is the midnight arrival of automatic tax increases, automatic spending cuts and the end of some unemployment benefits (all deadlines put in place by lawmakers back in 2011 during previous deficit-reduction and debt-ceiling negotiations).

Update at 7 p.m. ET. Senate May Vote Late Tonight

A deal may not come up for a vote in the Senate until after midnight, says Sen. Bob Corker, R-Tenn.

Update at 6:35 p.m. ET. House Adjourns Until Tuesday

The House adjourned for the day just before 6:30 p.m. ET; its next scheduled session begins at noon Tuesday.

Update at 5:15 p.m. ET. House In Limbo As Deadline Looms

Just after 5 p.m. ET, House Speaker John Boehner tweeted that Republican House Majority Whip Eric Cantor "has advised Members to stay near Capitol in case of further votes," leaving open the possibility that a vote may still come tonight. We've updated this post to reflect that news.

Update at 4:15 p.m. ET. No Vote In 2012?

The House will not hold a vote to avoid the "fiscal cliff" on Monday, Dec. 31 — the day before the first of the automatic budget cuts and higher taxes are due to take effect, according to reports.

Update at 2:55 p.m. ET. McConnell Says "We Are Very, Very Close":

Echoing many of the president's comments, McConnell just said on the Senate floor that "we are very, very close" on taxes. "Let's pass the tax relief portion now," he added, and "take what's been agreed to and keep moving."

NPR's Scott Horsley reports that according to "people familiar the negotiations," the key components of the emerging deal on taxes are the extension of Bush-era tax cuts for individuals earning less than $400,000 a year and couples earning more than $450,000. Income above those levels would be taxed at a 39.6 percent rate.

Update at 1:55 p.m. ET. Can Accomplish Most Important Goal:

Toward the end of his comments, the president says the primary goal of the talks now is to "stop taxes going up for middle class families starting tomorrow." That is, he says, "a modest goal we can accomplish."

And he jokes that "if there's even one second left before you have to do what you're supposed to do," members of Congress "will use that last second."

Update at 1:52 p.m. ET. Another Hint About Solving This In Steps:

The president talks about the automatic spending cuts set to kick in at midnight and speaks in the future tense: "Any agreement we have to deal with automatic spending cuts ... those also have to be balanced. ... Revenues have to be part of the equation in turning off the 'sequester.' "

Update at 1:48 p.m. ET. Solution "In Stages":

Hinting that there won't be a deal that covers every aspect of the fiscal cliff, the president says "it may be we can do it in stages."

Update at 1:46 p.m. ET. Agreement Is "Within Sight," But Not Done:

"I do need to talk about the progress that's being made in Congress today," Obama says. An agreement is "within sight ... but it's not done."

Update at 1:42 p.m. ET. Starting Shortly:

A group of people — likely to be described by the White House as Americans who would benefit from a deal to avoid going over the "cliff," have gathered behind the podium from which the president will speak.

Update at 1:25 p.m. ET. Expect To Hear "Outlines" Of A Deal?

On the NPR broadcast, correspondent John Ydstie just said it's now believed the president will announce the outlines of a deal. As correspondent Julie Rovner added, the plan will still need to be voted on in both the House and Senate and that might not happen until after midnight. But John noted that Congress could let provisions go into effect retroactively. That is, the federal government might technically go over the "fiscal cliff," but be pulled back up later by legislation.

"On taxes, one of the thorniest issues on the table, the two sides appeared to be converging. President Barack Obama has called for raising individual income-tax rates on family income above $250,000. In the latest round of Senate talks, Republicans proposed a $550,000 threshold, which Democrats moved to $450,000, according to Sen. Dick Durbin (D., Ill.)."

"McConnell and Biden, who served in the Senate together for 23 years, are closing in on an agreement that would hike tax rates for families who earn more than $450,000, and individuals who make more than $400,000, according to sources familiar with talks. That would mark significant concessions for both men, particularly for McConnell. President Barack Obama campaigned on raising taxes for families who make more than $250,000, but McConnell has long been dead-set against any tax increases, warning they would jeopardize the economy."

As the Journal adds, though:

"Before noon on Monday, Senate Majority Leader Harry Reid (D., Nev.) said on the Senate floor that discussions continue, but he also warned 'we really are running out of time,' adding that 'There are a number of issues on which the two sides are still apart.' "